允许的$β$光谱形状的高精度分析描述
High precision analytical description of the allowed $β$ spectrum shape
摘要：
考虑到正在进行的和计划的测量，给出了允许的$β$频谱形状的全面分析描述。它的研究形成了一个宝贵的工具，在寻找物理超越标准电弱模型和弱磁反冲项。来自有限尺寸修正，质量效应和辐射修正的贡献进行审查。一个特别的重点放在原子和化学效应，现有的描述是扩展和分析提供。讨论了QCD引起的反冲项的影响，并对不同的理论形式进行了交叉检验。特别注意的是比较处理原子核结构的影响，在不同的形式。费米和Gamow-Teller跃迁的修正，并彻底讨论了分析评估的方法。在积分形式下，计算的$f$值与目标精度范围内最精确的数值结果一致。我们强调需要一个准确的评估弱磁性的贡献，并注意到经常被忽视的诱导赝标相互作用的可能意义。与改进的原子校正，然后，我们提出了一个分析描述的允许$β$光谱形状精确到几个部分在$10^{-4}$下降到1\，千电子伏的低到中等$Z$核，从而延长了近一个数量级的工作由以前的作者。
英文摘要：
A fully analytical description of the allowed $β$ spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. A particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated $f$ values were in agreement with the most precise numerical results within the aimed for precision. We stress the need for an accurate evaluation of weak magnetism contributions, and note the possible significance of the oft-neglected induced pseudoscalar interaction. Together with improved atomic corrections, we then present an analytical description of the allowed $β$ spectrum shape accurate to a few parts in $10^{-4}$ down to 1\,keV for low to medium $Z$ nuclei, thereby extending the work by previous authors by nearly an order of magnitude.
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